Related papers: Public-key cryptography and invariant theory

Two different kinds of synchronization have been applied to cryptography: Synchronization of chaotic maps by one common external signal and synchronization of neural networks by mutual learning. By combining these two mechanisms, where the…

We present several quantum public-key encryption (QPKE) protocols designed with conjugate coding single-photon string, thus may be realized in laboratory with nowadays techniques. Two of these schemes are orienting one-bit message, and are…

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.

In this paper, we suggest a code-based public key encryption scheme, called McNie. McNie is a hybrid version of the McEliece and Niederreiter cryptosystems and its security is reduced to the hard problem of syndrome decoding. The public key…

Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes…

Two recently published papers propose some very simple key distribution schemes designed to enable two or more parties to establish a shared secret key with the aid of a third party. Unfortunately, as we show, most of the schemes are…

We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…

In 2019 G\'omez described a new public key cryptography scheme based on ideas from multivariate public key cryptography using hidden irreducible polynomials. We show that the scheme's design has a flaw which lets an attacker recover the…

Recently, the invention of quantum computers was so revolutionary that they bring transformative challenges in a variety of fields, especially for the traditional cryptographic blockchain, and it may become a real thread for most of the…

At Eurocrypt'99, Paillier presented a public-key cryptosystem based on a novel computational problem. It has interested many researchers because it was additively homomorphic. In this paper, we show that there is a big difference between…

Lectures on classical and quantum cryptography. Contents: Private key cryptosystems. Elements of number theory. Public key cryptography and RSA cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty relations. The no…

Polycyclic groups are natural generalizations of cyclic groups but with more complicated algorithmic properties. They are finitely presented and the word, conjugacy, and isomorphism decision problems are all solvable in these groups.…

In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…

A concept named induced trapdoor one-way quantum transformation (OWQT) has been introduced, and a theoretical framework of public-key encryption (PKE) of quantum message is presented based on it. Then several kinds of quantum public-key…

A quantum key distribution scheme whose security depends on the features of pre- and post-selected quantum states is described.

In 1999, public key cryptography using the matrix was devised by a hish school student of 16 yesrs old girl Sarah Flannery. This cryptosystem seemed faster than RSA, and it's having the strength to surpass even the encryption to RSA.…

We present a quantum version of a cipher used in cryptography where the message to be communicated is encoded into the relative phase of a quantum state using the shared key. The encoded quantum information carrying the message is actually…